Unraveling the Concept of Relativity: Understanding Light and Time

[Gear300]

Over time, I've realized there are certain limits to how far the human imagination can go. Even for simple things, it seems that we can not imagine much further than what experience allows...anyways: How does this light and time thing work? How is it that time slows down as we go faster?? It doesn't seem all too hard for me to imagine going faster than a beam of light...and why is light constant...and why at 3.00 X 10E8 m/s...?

 

[Fredrik]

and why is light constant...and why at 3.00 X 10E8 m/s...?

No one knows.

How is it that time slows down as we go faster??

That's a consequence of the fact that the speed of light doesn't depend on the speed of the light source. Imagine a spaceship moving with velocity v relative to you, and suppose they switch on a laser with the beam going perpendicular to the direction of their motion (from their point of view), and hitting a target inside the ship.

To them, the distance between the light source and the target is ct, where t is the time it takes the light to reach the target according to their clock. But from your point of view, the ship will have moved a distance vt' when the laser hits the target, where t' is the time it takes the light to reach the target according to your clock. So from your point of view, the light had to travel a greater distance to reach its target. That distance is ct'.

But ct', vt' and ct are not independent of each other. The relationship between them is described by the Pythagorean theorem, since ct' is the hypothenuse of a right triangle, so we have

$$(ct')^2=(vt')^2+(ct)^2$$

If you solve this for t, the result is

$$t=t'\sqrt{1-\frac{v^2}{c^2}}$$

which is <t' since that square root is <1.

 

[Gear300]

...I see. You've seemed to have answered my question...it makes sense. But just to give purpose to...why does time slow down when we go faster? Is it because while moving, the energy dimensionally stresses space...and to that extent...time?

 

[Mentz114]

why does time slow down when we go faster?

your clocks will appear slower to someone who is moving relative to you. You won't notice anything different. The reason, as Frederik has indicated, is because the speed of light is the same for both ( and all) observers.

 

[Fredrik]

I don't think I can come up with a better answer than the one I already gave you. It has nothing to do with energy. Neither space nor time needs to be "stressed" in any way for this effect to appear.

This is one way to think of it: A clock is a device that measures the "length" of its own path through space-time, with "length" defined in a strange way. To calculate it, you could break the path up into a series of short jumps and then add up contributions of the form $\sqrt{c^2dt^2-dx^2-dy^2-dz^2}$ along the path. The dx, dy and dz are all =0 along the path through space-time of a clock that's stationary in space, so a stationary clock takes the "longest" possible path through space-time.

Note that c is the upper speed limit on massive particles and that the presence of c in that square root implies that a higher value of c would make the contribution from dx, dy and dz less significant. So if there was no upper speed limit (i.e. if we take the limit $c\rightarrow\infty$) all paths between the same two endpoints would have exactly the same "length", and there would be no time dilation.

 

[Gear300]

Interesting stuff...its beginning to make a little bit of sense to me now...